The broad objective of this research program is to determine the biophysical and cellular substrate of the velocity storage neural integrator (VSNI) in the vestibulo-oculomotor system. Existing neural models of vestibular integrators rely largely on recurrent positive feedback networks to implement the integration. Anatomic evidence for the requisite recurrent axon collateral feedback in identified integrator neurons in goldfish and in mammals, however, is lacking. Preliminary analyses suggest that VSNI neurons behave as fractional order integrators; however, neither fractional nor integrative dynamical behaviors is presently understood at the neural level. The proposed research will develop the mathematical, analytic and methodological techniques to be used in a subsequent larger study of the relative contributions of cellular and network properties to velocity storage neural integration. The specific aims are (1) to test the hypothesis that VSNI neurons in goldfish are fractional order integrators, and quantify their integrative properties; (2) to test the hypothesis that the observed range of branching geometries and heterogeneity of dendritic process types in Area II neurons is causally related to the diversity of observed response dynamics; (3) to abstract the contributions of dendritic branching topology, dendritic nonuniformity and intrinsic membrane currents to fractional and integrative response dynamics via biophysically realistic modeling of VSNI neurons. The expected results are: characterization of the range of integrative response dynamics in VSNI neurons; correlation between fractal structural properties and possibly fractional integrative response dynamics and an estimate of the relative roles of intrinsic structural and cellular factors in producing these dynamics. The unique features of this project are (1) use of the goldfish preparation in which velocity storage neurons are easily identified, finite in number for realistic modeling and structure-function experiments that include both single cell sharp and patch electrode recordings; (2) use of new mathematical methods for relating fractional integrative dynamics to fractal dendritic structures, including computation of 3-D fractal dimension and new analytic techniques for deriving fractional differential equations from their physical substrates. This research will provide the methodology and pilot results for future model-based studies of the neural basis of velocity storage and angular VOR spatial orientation. These results will impact on current system-level models of vestibulo-ocular function, and on general theoretical models of persistent neural activity and short-term memory in multiple areas of neuroscience.